Product Instructions: Dynamics Trolley
FO90710
The Dynamics Trolley is intended for mechanics investigations, including linear momentum,
velocity and acceleration.
The apparatus consists of a wooden body carried on a three low friction plastic wheels, with a
strong spring plunger for “explosion” experiments. The plunger can be pushed in by hand, and
pushed upwards so it is contained by the metal plate.
It is supplied with three dowel plugs, the shorter of which fits to the front of the trolley and is
used as a trigger for the spring plunger. The plunger is release by a sharp tap on the top of the
dowel.
The other pieces of dowel can be used to stack trolleys as required, by fitting the dowel into the
corresponding holes on the top and bottom of the trolley, as illustrated above. By stacking, the
effective mass of a trolley is doubled or tripled. Extra mass can be placed on the flat top of the
trolleys as required.
Two corks are also supplied which fit into the holes
drilled into the front of the trolley. If long pins are
stuck into the cork, then when one trolley impacts
with another, they should stick together, thus allowing
investigation into inelastic collisions.
Timing is by way of a ticker timer and tape. The tape is attached to the rear of the trolley.
Suitable ticker timers are available from Timstar, catalogue codes FO81625 (tape FO81626)
or FO81650 (tape FO81651).
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Product Instructions: Dynamics Trolley
Experiment 1
The purpose of this experiment is to demonstrate the acceleration of a trolley down an inclined
plane.
It requires a dynamics trolley, a ramp/runway, and a ticker timer with suitable power supply and
leads.
Ensure that the track is clean and free from grit and debris, as this will produce surprisingly large
errors in your results.
1.Set up the runway with one end raised using bricks, books, or something else suitable.
An angle between 3° and 12° is suitable according to preference.
2. Set up the ticker timer at the top of the ramp
3.Place the trolley at the top of the ramp, immediately in front of the timer with a small bock
of wood or similar to prevent it from rolling down
4.Take a suitable length of ticker tape and pass it through the timer, attaching the end to the
rear of the trolley with adhesive tape
5.Switch on the ticker timer and allow the trolley to run down the slope
Because the timer is supplied with AC at 50Hz (mains frequency), it produces a dot on the paper
every 50th of a second (or 20ms = 0.02s). Therefore, the distance between each dot is the
distance travelled by the trolley in 0.02s.
speed=distancetime
D
In the example above, the distance D is measured to be 0.011m, so the speed at which the
vehicle was going at this time was:
speed=0.011m0.02s=0.55
-1
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Product Instructions: Dynamics Trolley
The ticker tape makes it very easy to plot speed against time. Cut the ticker tape at the position of
the 5th mark, and every 5 marks after that. Keep the cut lengths of tape in order.
Each 5 dots on the tape, and therefore each length of tape cut, represents 1/10th of a second.
The length of the tape is the distance travelled in that time, and is therefore proportional to the
speed.
Draw a set of axes, with time as the x-axis and speed as the y-axis. Starting with the first length of
cut tape, place the pieces side by side along the time axis.
sp
ee
time
It can be seen that, if the corresponding points on each length of tape are “joined up”, then a
straight line graph is drawn. The slope of this graph is the acceleration of the trolley.
If the graph “levels off” with time (i.e. the trolley no longer gets faster with time) it is because
of frictional losses which counteract the acceleration due to gravity. The friction increases with
speed, so this effect will become more apparent as speed increases.
The effect of friction can be reduced by making the slope steeper.
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Product Instructions: Dynamics Trolley
Experiment 2
The purpose of this experiment is to investigate the effect of different accelerating forces on
different masses.
It requires two or three dynamics trolleys, a ramp/runway, a bench mounting pulley, some cord,
some slotted masses on a hanger, and a ticker timer with suitable power supply and leads.
1. Place the ramp near the edge of the bench
2.Raise the far end of the ramp slightly, to overcome friction – the correct angle of
compensation is when the trolley runs down the ramp at a constant speed when given a
gentle push to start it
3.Place the ticker timer at the raised end of the ramp
4.Attach a pulley to the bench at the other end of the ramp
5.Put the trolley at the top of the ramp – it should not roll if the ramp isn’t too steep
6.Attach a length of cord to the front of the trolley, of sufficient length to span the length of
the ramp and go over the pulley
7.Secure the trolley, and attach a mass hanger to the free end of the cord
8.Take a suitable length of ticker tape, pass it through the time, and attach it to the back of
the trolley
9.Start the timer, and allow the trolley to roll freely down the ramp
Trolley
Cord
Pulley
Mass
10. Repeat the experiment with:
a) an additional trolley stacked on the first
b) one trolley with twice the original mass suspended from the cord
c)an additional trolley stacked on the first and twice the original mass suspended from
the cord
d) (b) and (c) with three times the original mass suspended from the cord
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Product Instructions: Dynamics Trolley
The force diagram for this setup is:
N
T
mg
However, the ramp is raised such that the friction is compensated for by the component of the
weight parallel to the ramp, so the force diagram can be redrawn like so:
N
T
mgcos
The normal reaction N is equal and opposite to the component of the weight normal to the
ramp, mgcos, where is the incline of the ramp.
The tension T of the cord has magnitude equal to the weight of the mass M suspended from the
cord.
Newton’s second law tells us:
F: force
=m: mass
a: acceleration
We know the force to be =, so the acceleration of the trolley is given by:
=
Acceleration is proportional to the mass pulling it, and inversely proportional to its own mass.
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Product Instructions: Dynamics Trolley
A specimen of results can be seen below.
The speed of the trolley is proportional to the distance between the dots on the tape, and the
length of the tape is the distance travelled.
If the distance between the dots is greater at the end of similar lengths of tape, the speed of the
trolley was greater when it reached the end of the ramp, and therefore it experienced a greater
acceleration.
1
1 trolley
2
1 trolley
3
1 trolley
1
2 trolleys
2
2 trolleys
3
2 trolleys
If desired, the tape from each experiment can be cut and stuck onto set of axes as done in
experiment 1, however, this can be quite time consuming, and it is a good exercise to analyse
results directly from the ticker tape.
1.Measure the distance between the first dot and the last dot – this is the distance travelled
by the trolley
2.Measure the distance between the last dot and the penultimate dot, and divide by 0.02s to
get the final speed.
3.You can now calculate the acceleration using a suvat equation:
2= 2+2
We know the initial velocity =0, so:
= 22
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Product Instructions: Dynamics Trolley
Measure the acceleration from the lengths of ticker tape, and record the results in a table like so:
Accelerating Mass
Acceleration
1
2
3
1
Trolley mass
2
By comparing the accelerations for different accelerating masses and trolley masses, it can be
seen that the results agree with Newton’s second law.
Rearrange the following equation to make acceleration under gravity, g, the subject, and
substitute in the values from your table to find g:
a: acceleration
=M: accelerating mass
m: trolley mass
You should find that the acceleration under gravity is roughly the same in each case.
From this we can see that any number of different weights, when dropped, will accelerate at the
same rate and, therefore if they’re dropped from the same height at the same time, they will land
at the same time, regardless of their mass.
Astronaut David Randolph Scott, on the Apollo 15 mission, famously dropped a hammer
and feather on the moon at the same time, and they can be seen landing at the same time. This
experiment would not work on Earth because the feather would experience air resistance. Videos
of the experiment are freely available online.
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Product Instructions: Dynamics Trolley
Experiment 3
The purpose of this experiment is to investigate the effects of an elastic collision between trolleys,
and to observe and gain an appreciation of the conservation of momentum.
An elastic collision is one in which momentum is transferred entirely from one body to another.
In the special case where a moving body collides with a stationary body, the moving body will
stop and the stationary body will move off with the same speed and direction as the moving
body.
It requires two or three dynamics trolleys, a ramp/runway, a pair of magnets, and a ticker timer
with suitable power supply and leads.
1.Compensate the ramp for friction as in experiment 2, and set up the ticker timer at the top
end
2.On the top of each trolley, attach a magnet, such as a horseshoe or powerful neodymium,
such that the two trolleys will repel one another if brought close together
3.In the ticker timer, fit two carbon discs, and thread two lengths of ticker tape, with one
tape passing over the bottom disc, and the other under the top disc – this will result in
coincident marks on the tape
4.Position one trolley in front of the timer, and the other trolley about half way down the
ramp – lined up with their magnets facing
5.Attach the ends of the tapes, one to each trolley – you may wish to mark the tapes with a
number to identify them
6.Switch on the timer, and push the trolley at the top of the ramp gently so that it travels
towards the other at constant speed
7.Repeat the experiment with trolleys stacked with different mass ratios
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Product Instructions: Dynamics Trolley
In the following specimen results, the tape from the first trolley is on the left, and the tape from
the second is on the right. The order of events can be seen directly from the tape:
1. The first trolley is pushed off at constant speed
2.As it approaches the second trolley, it starts to slow down, and the second trolley starts to
accelerate
3.Eventually the first trolley stops completely, and the second trolley moves away at constant
speed
Trolley 2: 1 mass
Trolley 1: 1 mass
Trolley 2 finishes with the same speed as trolley 1 started
Trolley 2: 1 mass
Trolley 1: 2 masses
Trolley 2 finishes with twice the speed that trolley 1 started
Trolley 2: 1 mass
Trolley 1: 3 masses
Trolley 2 finishes with thrice the speed that trolley 1 started
Trolley 2: 2 masses
Trolley 1: 1 mass
Trolley 2 finishes with half the speed that trolley 1 started
Trolley 2: 3 masses
Trolley 1: 1 mass
Trolley 2 finishes with a third of the speed that trolley 1 started
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Product Instructions: Dynamics Trolley
If you watch the “collision” between the two trolleys, you’ll notice that they probably do not come
into physical contact, and that the momentum is transferred entirely by the interaction of the
magnets.
The force between two magnets is inversely proportional to the square of the distance:
α1
2
So, as the trolleys were close together, the repulsive force between them was very strong, and so
it’s very unlikely they’ll be able to come into contact before the momentum has transferred.
This makes for a very “efficient” collision, that is, one where little energy is lost as friction, sound,
heat etc.
Momentum is defined as the product of mass and velocity:
=
From this, you can work out the momentum of the trolleys before and after the collisions. You
should see that the momentum is the same, so we say that momentum is conserved.
Take the example of a trolley with mass colliding with a trolley with mass . The first trolley
approaches the second with velocity , and after the collision, the second trolley departs with
velocity 2.
Momentum before collision:
2 .+.0=2 .
Momentum after collision:
2 .0+ .2 = .2
We can see that the total momentum is the same before and after the collision. The same can be
done for the other elastic collisions.
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Product Instructions: Dynamics Trolley
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Product Instructions: Dynamics Trolley
Experiment 4
The purpose of this experiment is to investigate perfectly inelastic collisions.
An inelastic collision is one in which some kinetic energy is lost during the collision. It is
normally lost as sound, heat, or into deforming the objects involved. A perfectly inelastic
collision is one in which the maximum amount of kinetic energy is lost, in which case, the
colliding bodies stick together.
By using the corks and pins in the fronts of the trolleys,
we can create inelastic collisions. The kinetic energy is lost
in deforming the cork such that the pin sticks in it after
the collision.
It requires two or three dynamics trolleys, a ramp/runway,
and a ticker timer with suitable power supply and leads.
1.Compensate the ramp for friction as in experiment 2, and set up the ticker timer at the top
end of the ramp
2.Take two corks, and push a pin through the narrow end, such that the head of the pin is
nearly flush with the narrow end, and the sharp end of the pin sticks out of the wide end of
the cork
3. Fit the two corks with pins to one trolley, so that this trolley travels with two pins at the front
4. Fit another trolley with corks but without pins
5.Place one trolley at the top of the ramp, and the other half way along, such that when the
trolleys collide, the pin sticks into the cork
6.Thread a length of ticker tape through the timer and attach it to the back of the trolley at
the top of the ramp
7.Switch on the timer, and push the trolley at the top of the ramp gently so that it travels
towards the other at constant speed
8. Repeat the experiment with trolleys stacked with different mass ratios
From the conservation of momentum, we know that the momentum before the collision must
equal the momentum after the collision.
11+ 2 2= 1+2
As .2=0, the final velocity is given by:
11+ 2 1
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Product Instructions: Dynamics Trolley
In the following specimen results, the trolley can be seen to slow down instantly after colliding
with the second trolley.
In this example, one trolley collides with a second of equal mass. The distance between the dots
after the collision is half of that before, indicating the speed halves. The mass doubles, but the
speed halves, momentum is conserved.
Trolley 1: 1 mass
Trolley 2: 1 mass
Now, a trolley collides with a trolley of twice its mass. The distance between the dots after the
collision is a third of that before. The mass triples, but the speed reduces to one third of its
original, momentum is conserved.
Trolley 1: 1 mass
Trolley 2: 1 mass
Finally, a trolley collides with a trolley of half its mass. The distance between the dots after the
collision is two thirds of that before. The mass increases by half, and the speed reduces by a
third.
Trolley 1: 1 mass
Trolley 2: 1 mass
Momentum before:
2 .+.0=2 .
Momentum after:
3 .23 =2. .
Momentum after the collision is the same as momentum before the collision, therefore,
momentum is conserved.
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Product Instructions: Dynamics Trolley
Experiment 5
The purpose of this experiment is to investigate the distribution of momentum between trolleys
forced apart by “explosion”.
Because it involves trolleys moving in different directions, ticker tape is not a practical timing
method. Instead, a data logger and two sound sensors can be used to detect when trolleys
impact with wooden blocks at either end of the ramp.
It requires two or three dynamics trolleys, a ramp/runway, a data logger and two sound sensors.
1.Place the runway on a level surface. It is impossible to compensate for frictions as the
trolleys will move in opposite directions.
2. Insert a dowel peg into one of the trolleys, in the hole above the plunger
3.“Prime” the trolleys by pushing the spring loaded plunger into the body, and securing it
behind the metal plate.
“Primed”
4.Place the trolleys at the centre of the runway, with a wooden block at each end, and sound
sensor attached to each block
5.Start the data logger with an interval of 1ms (1kHz), and strike the dowel peg on the top
with a hammer – this releases the plunger sending the trolleys in opposite directions
6. Stop the data logger when the trolleys have hit their end blocks
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Product Instructions: Dynamics Trolley
It may be necessary to adjust the position of the trolleys and end blocks such that they hit their
respective blocks at the same time.
Compare the two sets of data from the sound sensor. The first peak is the sound from when the
hammer struck the trolley, and when they were released. The second peak is when the trolley hit
the block that the sound sensor is attached to.
IMAGE OF CHART
REQUIRED
IMAGE OF CHART
REQUIRED
Your data may look significantly different from this, depending on how hard you hit the trolley, on
the background noise, and on echoes. However, the important events should be clearly visible.
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Product Instructions: Dynamics Trolley
If the two trolleys travel the same distance in the same time, then they have travelled at the same
speed.
As neither of the trolleys was moving before the “explosion”, the momentum is zero.
Momentum before:
1.0+ 2.0=0
Momentum after:
1. 1+2. 2
If both trolleys travelled the same distance in the same time, then their speeds were the same, but
in the opposite direction, so: 2=1 1:
Momentum after:
1. 1-
2. 1=0
So it is possible for a system to have moving particles, but for the total momentum of that system
to be zero.
The momentum before and after the explosion is zero, so momentum is conserved.
This experiment can be repeated with trolleys of different masses.
It should be noted that, because it is impossible to compensate for friction, accurate results are
difficult to achieve, making this more of a qualitative experiments.
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Product Instructions: Dynamics Trolley
The experiments described in this manual are intended only as a brief guide to the types of
investigation possible.
Dynamics trolleys are very versatile, and the range of experiments possible with them and their
accessories goes far beyond the scope of this manual.
Use the following pages to record any links to online experiments, or your own experimental
notes.
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Product Instructions: Dynamics Trolley
Notes
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Product Instructions: Dynamics Trolley
Notes
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Product Instructions: Dynamics Trolley
Associated Equipment
Ticker Timers
Value Version
FO81625
Ticker Tape 30m x 15mm
FO81626
40mm carbon paper discs
FO81627
Premium Version
FO81650
Ticker Tape 30m x 9.5mm
FO81651
50mm Carbon Paper Discs
FO81652
Pulleys and Cord
50mm Bench Mounting Pulley
PU12720
70mm Bench Mounting Pulley
PU12722
Red Cotton Twine
ST96250
Braided Nylon Cord (Black)
PU105150
Braided Nylon Cord (White)
PU105152
Runways/Ramps
1.2m
FO91711
1.5m
FO91714
2.4m
FO91712
Run-off Ramp
FO71704
Track Support
FO71706
Magnets
“Alnico” Horseshow Magnet
MA10145
Data Logging
The uLog Sound Sensor plugs directly into your computer’s USB port, and includes software
for collecting and analysing data. Two sound sensors can be used at once to record sound at
different places.
uLog Sound Sensor
DA114020
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